Responses of the haploid-to-diploid ratio of isomorphic biphasic life cycles to time instability

Abstract

Previous modelling of the haploid-to-diploid ratio (H:D) in biphasic life cycles relied on estimates of the stable population growth rate and structure. This is a projective analysis that estimates the population dynamics given current conditions. However, the environment is rarely constant and has both periodicity and random instabilities. The objective of this work was to unveil how the H:D responds to them. It was found that ploidy phase dissimilarities on the demographic matrix and/or in the initial population structure cause an inevitable H:D time variability as a consequence of the life-cycle structure and independent of the environmental seasonal cycle. This variability depends on the type of life strategy, demographic processes involved and ploidy dissimilar vital rates. Furthermore, ploidy dissimilar fertility or growth rates cause cyclic oscillations mismatching the seasonal cycle, whereas ploidy dissimilarities in the ramet looping rates (survival related) induce a monotonical variation.

Regulation of the Demographic Structure in Isomorphic Biphasic Life Cycles at the Spatial Fine Scale

“…Then, in populations with looping life strategies the H:D patches formed show great constancy, whereas in populations with fertility or growth life strategies the patches may oscillate backward and forward at a fast rate. A similar transient behaviour was obtained in Vieira and Santos [18] for the non-spatial case.…”

“…The Gelidium sesquipedale 's estimated demography corresponds to those predicted by Vieira and Santos [18] , [24] being approximately evenly elastic to fertility, growth and looping rates. In these, individuals flow mainly through the shortest life-cycle loop generating short period oscillations on both λ and the H:D quickly damping away.…”

“…However, the demographic matrix was generalized for parsimony and not adjusted to any particular population or species (equation 1): (i) the haploid and diploid fecundities (fec) were dependent on the parameters f H and f D and a size class weight factor ( wf j , j is the column index) accounting for allometry; (ii) the survival of the carpospores ( S carp ) and of the tetraspores ( S tet ) was kept constant; (iii) the haploid and diploid ramet growth rates were dependent on the parameters g H and g D ; (iv) the haploid and diploid stasis, breakage and clonal growth were aggregated as looping rates and dependent on the parameters l H and l D . It was named “looping” for consistency with previous works by Vieira and Santos [18] , [19] , [24] and is equivalent to retrogression plus stasis [25] , [26] , [27] . All ramet stages of the same ploidy had the same amount of looping.…”

“…This type of classification was introduced in plant demography by Franco and Silvertown [29] and Oostermeijer et al [25] . It was later applied to the demography of isomorphic biphasic life cycles in Vieira and Santos [18] , [19] , [24] .…”

“…[2] , Otaiza et al [17] and Thornber and Gaines [3] . Nevertheless, using a theoretical modeling approach, Vieira and Santos [18] have determined cyclic alternations in phase dominance may arise as a sole consequence of a ploidy asymmetrical life cycle structure with fixed ploidy differences in features like size of first reproduction or maximum frond size. Habitats also change widely with geographical location and the H:D of a particular species changes accordingly [3] , [7] .…”